Showing 1–50 of 129 results for author: Turner, R E

Earth observation embeddings are effective sub-grid descriptors for probabilistic weather downscaling

Authors: Pedro Sousa, Will Tebbutt, Sadiq Jaffer, Robin Young, Anil Madhavapeddy, Richard E. Turner

Abstract: Global weather reanalyses and forecasts resolve the evolving atmospheric state on coarse grids, but site-specific applications require predictions at arbitrary locations where near-surface conditions also depend on unresolved terrain and land-surface properties. Existing probabilistic downscalers address this gap using hand-crafted topographic descriptors. We ask instead whether Earth observation… ▽ More Global weather reanalyses and forecasts resolve the evolving atmospheric state on coarse grids, but site-specific applications require predictions at arbitrary locations where near-surface conditions also depend on unresolved terrain and land-surface properties. Existing probabilistic downscalers address this gap using hand-crafted topographic descriptors. We ask instead whether Earth observation foundation models can provide transferable sub-grid surface representations for probabilistic weather downscaling. We augment a convolutional conditional neural process that downscales coarse ERA5 reanalysis fields at ~25 km resolution with a learned local surface descriptor, obtained by compressing a patch of TESSERA embeddings at 10 m resolution. Although these embeddings summarise surface conditions over annual timescales, they improve downscaling of instantaneous 2 m temperature and 10 m wind speed by encoding persistent surface properties that capture a location's departure from the coarse-grid atmospheric state. Across five climatically diverse regions, the embedding improves point and probabilistic skill at stations held out in both space and time, overall improving CRPS skill by 11.5% for 2 m temperature and 6.2% for 10 m wind speed. We further analyse how its contribution differs by variable, finding that topography explains more of temperature's sub-grid structure, while TESSERA provides additional surface information for wind speed. These improvements persist when the coarse input is changed from ERA5 to forecasts from the Aurora AI forecasting model, and when predicting at newly deployed stations with no regional history. To our knowledge, this is the first evidence that long-timescale Earth-observation embeddings can support short-timescale weather downscaling where sub-grid departures are systematically structured by persistent surface properties. △ Less

Submitted 12 August, 2026; originally announced August 2026.

Comments: 39 pages, 12 figures, 6 tables

AIFS-TC: A simple correction competitive with the operational frontier for tropical cyclone intensity forecasting

Authors: Anna Allen, Wessel P. Bruinsma, Michael Maier-Gerber, Harrison Cook, Matthew Chantry, Richard E. Turner

Abstract: AI weather models are in the process of revolutionising weather forecasting. While these models have been shown to achieve superior performance to physics-based NWP in forecasting tropical cyclone (TC) tracks, they tend to dramatically underestimate intensity. Here we present AIFS-TC, a simple correction to the AIFS-Single model that is competitive with the operational state-of-the-art for forecas… ▽ More AI weather models are in the process of revolutionising weather forecasting. While these models have been shown to achieve superior performance to physics-based NWP in forecasting tropical cyclone (TC) tracks, they tend to dramatically underestimate intensity. Here we present AIFS-TC, a simple correction to the AIFS-Single model that is competitive with the operational state-of-the-art for forecasting maximum wind speed and minimum central pressure at lead times of 12 h to seven days. This performance also holds for rapid intensification events. Notably, the entire system was autonomously designed and built by a large language model (Claude Fable 5) in a few hours, directed through a small number of natural-language prompts by a single domain scientist. That the operational frontier can be reached with an open-source AI forecast model (AIFS-Single) and relatively simple, cheap post-processing is significant for TC science, and points to agentic coding as a route to rapid exploration and progress in life-saving early-warning systems in other domains. △ Less

Submitted 13 August, 2026; v1 submitted 24 July, 2026; originally announced August 2026.

Comments: 6 pages, 5 figures, 2 tables

Otter Weather: Skillful and Computationally Efficient Medium-Range Weather Forecasting

Authors: Cristiana Diaconu, Jonas Scholz, Aliaksandra Shysheya, Stratis Markou, Payel Mukhopadhyay, Miles Cranmer, Richard E. Turner

Abstract: State-of-the-art medium-range AI weather models can outperform traditional Numerical Weather Prediction (NWP) but require massive training budgets. This restricts usage for under-resourced groups and severely limits fast model iteration. Here we develop Otter Weather, a highly efficient spatiotemporal forecasting model designed to democratise high-performance weather prediction with AI. Evaluated… ▽ More State-of-the-art medium-range AI weather models can outperform traditional Numerical Weather Prediction (NWP) but require massive training budgets. This restricts usage for under-resourced groups and severely limits fast model iteration. Here we develop Otter Weather, a highly efficient spatiotemporal forecasting model designed to democratise high-performance weather prediction with AI. Evaluated on ERA5 reanalysis data at 1.5° resolution using standard WeatherBench protocols, the Otter family significantly advances the skill-compute Pareto frontier. The deterministic version outperforms the best NWP baseline by 9.6% at a 24-hour lead time while requiring fewer than 3.5 A100-days for training. It provides a 2x efficiency gain over lightweight AI models and a 100-fold reduction in compute compared to resource-intensive frontier architectures. We extend these efficiency gains into probabilistic forecasting by training via the Continuous Ranked Probability Score (CRPS). Scaling to a larger architecture, Otter-XL achieves a 9.7% CRPS improvement over the IFS ENS baseline. This yields an almost two-fold increase in predictive skill over comparable lightweight models at similar compute budgets. Otter-XL also outperforms frontier architectures like GenCast by over 2%, while using an order of magnitude less compute. Finally, Otter is applied out-of-the-box to a complex acoustic scattering PDE task where it outperforms a state-of-the-art foundation modelling approach, suggesting that the advances made here might apply across a range of scientific domains. △ Less

Submitted 24 June, 2026; originally announced June 2026.

Recursively Trained Diffusion Models: Limiting Collapse Distribution and Spectral Characterization

Authors: Naïl B. Khelifa, Richard E. Turner, Ramji Venkataramanan

Abstract: Recursive training of generative models on their own outputs can lead to model collapse, a compounding drift away from the true data distribution. Existing theoretical works bound finite-round error accumulation in the context of diffusion models, but two questions remain open:~what distribution does the recursion converge to, and how fast? We answer both, isolating a mechanism distinct from imper… ▽ More Recursive training of generative models on their own outputs can lead to model collapse, a compounding drift away from the true data distribution. Existing theoretical works bound finite-round error accumulation in the context of diffusion models, but two questions remain open:~what distribution does the recursion converge to, and how fast? We answer both, isolating a mechanism distinct from imperfect learning: even with perfect score estimation and exact sampling, the early stopping of the reverse diffusion (required for numerical stability) drives a progressive drift away from the data distribution. We prove that this recursion converges geometrically to a unique limiting distribution, which admits a closed-form characterization as an infinite mixture of increasingly Gaussian-smoothed versions of the data distribution. A Hermite spectral decomposition of this limit reveals that recursive training acts as a low-pass filter: higher-order modes, which encode fine non-Gaussian structure, are attenuated much more strongly than coarse modes. This spectral picture motivates annealed truncation schedules that progressively shrink truncation times across retraining rounds; we prove that any schedule converging to $0$ asymptotically eliminates recursive compounding. Finally, we show our idealized characterization is robust: in the presence of discretization and score estimation errors, the learned distribution remains in a Wasserstein-2 ball around the ideal limit, with mode-dependent contraction rates that contract high-order errors faster than low-order ones. We validate the theory on synthetic Gaussian mixtures and CIFAR-10. △ Less

Submitted 11 June, 2026; originally announced June 2026.

Diffusion Models Observe Only Gradients: A Geometric Perspective on Score Matching Errors

Authors: Naïl B. Khelifa, Richard E. Turner, Ramji Venkataramanan

Abstract: Score-based diffusion models are typically trained by minimizing the $L^2$ score matching error, and standard theoretical analyses rely on this quantity to bound the sampling discrepancy between the learned and target distributions. We show the $L^2$ score error is not the right intrinsic measure of marginal distributional quality: a learned diffusion model can incur arbitrarily large $L^2$ score… ▽ More Score-based diffusion models are typically trained by minimizing the $L^2$ score matching error, and standard theoretical analyses rely on this quantity to bound the sampling discrepancy between the learned and target distributions. We show the $L^2$ score error is not the right intrinsic measure of marginal distributional quality: a learned diffusion model can incur arbitrarily large $L^2$ score error while perfectly matching the target distribution. By decomposing score errors into a gradient and a solenoidal component (a Helmholtz-Hodge decomposition), we identify the geometric reason behind this: only the gradient component enters the marginal Fokker-Planck dynamics, while the solenoidal component is structurally invisible. We make this precise in three results. First, building on the corrected geometry, we prove an impossibility result: no monotone function of the $L^2$ score error can uniformly lower bound any divergence between the learned and target distributions. Second, we derive an upper bound on the Kullback-Leibler divergence that depends only on the observable gradient component of the error, tightening the standard Girsanov bound for generic score networks, and identifying its looseness as the cost of operating on path-space rather than marginal-space dynamics. Third, we give a tractable estimator of the gradient component via a dual Sobolev identity, which is shown to empirically correlate substantially better with sample quality than the full $L^2$ error. △ Less

Submitted 28 June, 2026; v1 submitted 4 June, 2026; originally announced June 2026.

Skillful high-resolution weather forecasting independent of physical models

Authors: Pengcheng Zhao, Siqi Xiang, Weixin Jin, Zekun Ni, Jiang Bian, Zuliang Fang, Hongyu Sun, Bin Zhang, Richard E. Turner, Jonathan Weyn, Haiyu Dong, Kit Thambiratnam, Qi Zhang

Abstract: Accurate and timely weather forecasts are critical for high-impact decisions in modern society. Machine-learning-based weather prediction is emerging as an alternative for producing initial conditions, forecasts, and even both in end-to-end systems. These methods deliver predictions faster and often with higher skill than traditional numerical weather prediction (NWP). However, even end-to-end mod… ▽ More Accurate and timely weather forecasts are critical for high-impact decisions in modern society. Machine-learning-based weather prediction is emerging as an alternative for producing initial conditions, forecasts, and even both in end-to-end systems. These methods deliver predictions faster and often with higher skill than traditional numerical weather prediction (NWP). However, even end-to-end models typically rely on NWP-generated reanalyses for supervision, thereby inheriting the biases and resolution limitations of those NWPs, and limiting adaptation to settings where suitable reanalysis products are unavailable, infrequently updated, or expensive to produce. Here we introduce ObsCast, a regional system that generates both analysis and predictions, without using any NWP-derived data in either training or inference, while still achieving state-of-the-art performance in short-term high-resolution regional modeling. Over the contiguous United States and Europe, ObsCast outperforms operational NWP for near-surface variables through 18 h and produces skillful precipitation forecasts. It provides a simpler and more adaptable route to build and refine regional forecasting services directly from local observations, without the need to develop complex and costly traditional forecasting pipelines. △ Less

Submitted 27 May, 2026; originally announced May 2026.

Comments: 26 pages, 10 figures

Probabilistic Retrofitting of Learned Simulators

Authors: Cristiana Diaconu, Miles Cranmer, Richard E. Turner, Tanya Marwah, Payel Mukhopadhyay

Abstract: Dominant approaches for modelling Partial Differential Equations (PDEs) rely on deterministic predictions, yet many physical systems of interest are inherently chaotic and uncertain. While training probabilistic models from scratch is possible, it is computationally expensive and fails to leverage the significant resources already invested in high-performing deterministic backbones. In this work,… ▽ More Dominant approaches for modelling Partial Differential Equations (PDEs) rely on deterministic predictions, yet many physical systems of interest are inherently chaotic and uncertain. While training probabilistic models from scratch is possible, it is computationally expensive and fails to leverage the significant resources already invested in high-performing deterministic backbones. In this work, we adopt a training-efficient strategy to transform pre-trained deterministic models into probabilistic ones via retrofitting with a proper scoring rule: the Continuous Ranked Probability Score (CRPS). Crucially, this approach is architecture-agnostic: it applies the same adaptation mechanism across distinct model backbones with minimal code modifications. The method proves highly effective across different scales of pre-training: for models trained on single dynamical systems, we achieve 20-54% reductions in rollout CRPS and up to 30% improvements in variance-normalised RMSE (VRMSE) relative to compute-matched deterministic fine-tuning. We further validate our approach on a PDE foundation model, trained on multiple systems and retrofitted on the dataset of interest, to show that our probabilistic adaptation yields an improvement of up to 40% in CRPS and up to 15% in VRMSE compared to deterministic fine-tuning. Validated across diverse architectures and dynamics, our results show that probabilistic PDE modelling need not require retraining from scratch, but can be unlocked from existing deterministic backbones with modest additional training cost. △ Less

Submitted 22 June, 2026; v1 submitted 2 March, 2026; originally announced March 2026.

Comments: Code provided at https://github.com/cddcam/lola_crps

Incremental Transformer Neural Processes

Authors: Philip Mortimer, Cristiana Diaconu, Tommy Rochussen, Bruno Mlodozeniec, Richard E. Turner

Abstract: Neural Processes (NPs), and specifically Transformer Neural Processes (TNPs), have demonstrated remarkable performance across tasks ranging from spatiotemporal forecasting to tabular data modelling. However, many of these applications are inherently sequential, involving continuous data streams such as real-time sensor readings or database updates. In such settings, models should support cheap, in… ▽ More Neural Processes (NPs), and specifically Transformer Neural Processes (TNPs), have demonstrated remarkable performance across tasks ranging from spatiotemporal forecasting to tabular data modelling. However, many of these applications are inherently sequential, involving continuous data streams such as real-time sensor readings or database updates. In such settings, models should support cheap, incremental updates rather than recomputing internal representations from scratch for every new observation -- a capability existing TNP variants lack. Drawing inspiration from Large Language Models, we introduce the Incremental TNP (incTNP). By leveraging causal masking, Key-Value (KV) caching, and a data-efficient autoregressive training strategy, incTNP matches the predictive performance of standard TNPs while reducing the computational cost of updates from quadratic to linear time complexity. We empirically evaluate our model on a range of synthetic and real-world tasks, including tabular regression and temperature prediction. Our results show that, surprisingly, incTNP delivers performance comparable to -- or better than -- non-causal TNPs while unlocking orders-of-magnitude speedups for sequential inference. Finally, we assess the consistency of the model's updates -- by adapting a metric of "implicit Bayesianness", we show that under a one-at-a-time streaming protocol, incTNP retains a prediction rule as implicitly Bayesian as standard non-causal TNPs, demonstrating that incTNP achieves the computational benefits of causal masking without sacrificing the consistency required for streaming inference. △ Less

Submitted 3 June, 2026; v1 submitted 21 February, 2026; originally announced February 2026.

Comments: Accepted at ICML 2026

Quantifying Error Propagation and Model Collapse in Diffusion Models

Authors: Nail B. Khelifa, Richard E. Turner, Ramji Venkataramanan

Abstract: Machine learning models are increasingly trained or fine-tuned on synthetic data. Recursively training on such data has been observed to significantly degrade performance in a wide range of tasks, often characterized by a progressive drift away from the target distribution. In this work, we theoretically analyze this phenomenon in the setting of score-based diffusion models. For a realistic pipeli… ▽ More Machine learning models are increasingly trained or fine-tuned on synthetic data. Recursively training on such data has been observed to significantly degrade performance in a wide range of tasks, often characterized by a progressive drift away from the target distribution. In this work, we theoretically analyze this phenomenon in the setting of score-based diffusion models. For a realistic pipeline where each training round uses a combination of synthetic data and fresh samples from the target distribution, we obtain upper and lower bounds on the accumulated divergence between the generated and target distributions. Notably, to the best of our knowledge, this is the first lower bound on the divergence between the learned and target distributions, even for standard diffusion models. Our results allow us to characterize different regimes of drift, depending on the score estimation error and the proportion of fresh data used in each generation. In a certain regime, the accumulated divergence after several retraining rounds can be expressed as a discounted sum of score estimation errors made at each generation. We also provide empirical results on synthetic data and images to illustrate the theory. △ Less

Submitted 28 May, 2026; v1 submitted 18 February, 2026; originally announced February 2026.

Comments: Accepted at ICML 2026

Probabilistic Modelling is Sufficient for Causal Inference

Authors: Bruno Mlodozeniec, David Krueger, Richard E. Turner

Abstract: Causal inference is a key research area in machine learning, yet confusion reigns over the tools needed to tackle it. There are prevalent claims in the machine learning literature that you need a bespoke causal framework or notation to answer causal questions. In this paper, we want to make it clear that you \emph{can} answer any causal inference question within the realm of probabilistic modellin… ▽ More Causal inference is a key research area in machine learning, yet confusion reigns over the tools needed to tackle it. There are prevalent claims in the machine learning literature that you need a bespoke causal framework or notation to answer causal questions. In this paper, we want to make it clear that you \emph{can} answer any causal inference question within the realm of probabilistic modelling and inference, without causal-specific tools or notation. Through concrete examples, we demonstrate how causal questions can be tackled by writing down the probability of everything. Lastly, we reinterpret causal tools as emerging from standard probabilistic modelling and inference, elucidating their necessity and utility. △ Less

Submitted 29 December, 2025; originally announced December 2025.

Journal ref: Proceedings of the 42nd International Conference on Machine Learning, PMLR 267:81810-81840, 2025

Artificial intelligence for methane detection: from continuous monitoring to verified mitigation

Authors: Gonzalo Mateo-Garcia, Anna Allen, Itziar Irakulis-Loitxate, Manuel Montesino-San Martin, Marc Watine, Cynthia Randles, Tharwat Mokalled, Alma Raunak, Carol Castañeda-Martinez, Juan E. Jonhson, Javier Gorroño, James Requeima, Claudio Cifarelli, Luis Guanter, Richard E. Turner, Manfredi Caltagirone

Abstract: Methane is a potent greenhouse gas, responsible for roughly 30% of warming since pre-industrial times. A small number of large point sources account for a disproportionate share of emissions, creating an opportunity for substantial reductions by targeting relatively few sites. Detection and attribution of large emissions at scale for notification to asset owners remains challenging. Here, we intro… ▽ More Methane is a potent greenhouse gas, responsible for roughly 30% of warming since pre-industrial times. A small number of large point sources account for a disproportionate share of emissions, creating an opportunity for substantial reductions by targeting relatively few sites. Detection and attribution of large emissions at scale for notification to asset owners remains challenging. Here, we introduce MARS-S2L, a machine learning model that detects methane emissions in publicly available multispectral satellite imagery. Trained on a manually curated dataset of over 80,000 images, the model provides high-resolution detections every two days, enabling facility-level attribution and identifying 78% of plumes with an 8% false positive rate at 697 previously unseen sites. Deployed operationally, MARS-S2L has issued 2,776 notifications to stakeholders in 25 countries, enabling verified, permanent mitigation of six persistent emitters, including a super-emitter in Algeria that had been releasing approximately 27,000 tonnes of methane annually for at least a decade and a previously unknown emitter in Libya first identified by MARS-S2L. These results demonstrate a scalable pathway from satellite detection to quantifiable methane mitigation. △ Less

Submitted 24 April, 2026; v1 submitted 26 November, 2025; originally announced November 2025.

Rotary Position Encodings for Graphs

Authors: Isaac Reid, Arijit Sehanobish, Cederik Höfs, Bruno Mlodozeniec, Leonhard Vulpius, Federico Barbero, Adrian Weller, Krzysztof Choromanski, Richard E. Turner, Petar Veličković

Abstract: We study the extent to which rotary position encodings (RoPE), a recent transformer position encoding algorithm broadly adopted in large language models (LLMs) and vision transformers (ViTs), can be applied to graph-structured data. We find that rotating tokens depending on the spectrum of the graph Laplacian efficiently injects structural information into the attention mechanism, boosting perform… ▽ More We study the extent to which rotary position encodings (RoPE), a recent transformer position encoding algorithm broadly adopted in large language models (LLMs) and vision transformers (ViTs), can be applied to graph-structured data. We find that rotating tokens depending on the spectrum of the graph Laplacian efficiently injects structural information into the attention mechanism, boosting performance in synthetic and real-world graph learning tasks. This approach, coined _Wave-Induced Rotary Encodings_ (WIRE), enjoys intriguing theoretical properties: it recovers regular RoPE on grids, and depends asymptotically on the graph effective resistance. Unlike bias-based relative position encodings, WIRE is compatible with linear attention. △ Less

Submitted 24 June, 2026; v1 submitted 26 September, 2025; originally announced September 2025.

Fresh in memory: Training-order recency is linearly encoded in language model activations

Authors: Dmitrii Krasheninnikov, Richard E. Turner, David Krueger

Abstract: We show that language models' activations linearly encode when information was learned during training. Our setup involves creating a model with a known training order by sequentially fine-tuning Llama-3.2-1B on six disjoint but otherwise similar datasets about named entities. We find that the average activations of test samples corresponding to the six training datasets encode the training order:… ▽ More We show that language models' activations linearly encode when information was learned during training. Our setup involves creating a model with a known training order by sequentially fine-tuning Llama-3.2-1B on six disjoint but otherwise similar datasets about named entities. We find that the average activations of test samples corresponding to the six training datasets encode the training order: when projected into a 2D subspace, these centroids are arranged exactly in the order of training and lie on a straight line. Further, we show that linear probes can accurately (~90%) distinguish "early" vs. "late" entities, generalizing to entities unseen during the probes' own training. The model can also be fine-tuned to explicitly report an unseen entity's training stage (~80% accuracy). Interestingly, the training-order encoding does not seem attributable to simple differences in activation magnitudes, losses, or model confidence. Our paper demonstrates that models are capable of differentiating information by its acquisition time, and carries significant implications for how they might manage conflicting data and respond to knowledge modifications. △ Less

Submitted 22 September, 2025; v1 submitted 17 September, 2025; originally announced September 2025.

Graph Random Features for Scalable Gaussian Processes

Authors: Matthew Zhang, Jihao Andreas Lin, Krzysztof Choromanski, Adrian Weller, Richard E. Turner, Isaac Reid

Abstract: We study the application of graph random features (GRFs) - a recently introduced stochastic estimator of graph node kernels - to scalable Gaussian processes on discrete input spaces. We prove that (under mild assumptions) Bayesian inference with GRFs enjoys $O(N^{3/2})$ time complexity with respect to the number of nodes $N$, compared to $O(N^3)$ for exact kernels. Substantial wall-clock speedups… ▽ More We study the application of graph random features (GRFs) - a recently introduced stochastic estimator of graph node kernels - to scalable Gaussian processes on discrete input spaces. We prove that (under mild assumptions) Bayesian inference with GRFs enjoys $O(N^{3/2})$ time complexity with respect to the number of nodes $N$, compared to $O(N^3)$ for exact kernels. Substantial wall-clock speedups and memory savings unlock Bayesian optimisation on graphs with over $10^6$ nodes on a single computer chip, whilst preserving competitive performance. △ Less

Submitted 25 September, 2025; v1 submitted 3 September, 2025; originally announced September 2025.

Warm Starts Accelerate Conditional Diffusion

Authors: Jonas Scholz, Richard E. Turner

Abstract: Generative models like diffusion and flow-matching create high-fidelity samples by progressively refining noise. The refinement process is notoriously slow, often requiring hundreds of function evaluations. We introduce Warm-Start Diffusion (WSD), a method that uses a simple, deterministic model to dramatically accelerate conditional generation by providing a better starting point. Instead of star… ▽ More Generative models like diffusion and flow-matching create high-fidelity samples by progressively refining noise. The refinement process is notoriously slow, often requiring hundreds of function evaluations. We introduce Warm-Start Diffusion (WSD), a method that uses a simple, deterministic model to dramatically accelerate conditional generation by providing a better starting point. Instead of starting generation from an uninformed $N(\boldsymbol{0}, I)$ prior, our deterministic warm-start model predicts an informed prior $N(\hat{\boldsymbolμ}_C, \text{diag}(\hat{\boldsymbolσ}^2_C))$, whose moments are conditioned on the input context $C$. This warm start substantially reduces the distance the generative process must traverse, and therefore the number of diffusion steps required, particularly when the context $C$ is strongly informative. WSD is applicable to any standard diffusion or flow matching algorithm, is orthogonal to and synergistic with other fast sampling techniques like efficient solvers, and is simple to implement. We test WSD in a variety of settings, and find that it substantially outperforms standard diffusion in the efficient sampling regime, generating realistic samples using only 4-6 function evaluations, and saturating performance with 10-12. △ Less

Submitted 29 September, 2025; v1 submitted 12 July, 2025; originally announced July 2025.

Comments: 10 pages, 6 figures

Estimating Interventional Distributions with Uncertain Causal Graphs through Meta-Learning

Authors: Anish Dhir, Cristiana Diaconu, Valentinian Mihai Lungu, James Requeima, Richard E. Turner, Mark van der Wilk

Abstract: In scientific domains -- from biology to the social sciences -- many questions boil down to \textit{What effect will we observe if we intervene on a particular variable?} If the causal relationships (e.g.~a causal graph) are known, it is possible to estimate the intervention distributions. In the absence of this domain knowledge, the causal structure must be discovered from the available observati… ▽ More In scientific domains -- from biology to the social sciences -- many questions boil down to \textit{What effect will we observe if we intervene on a particular variable?} If the causal relationships (e.g.~a causal graph) are known, it is possible to estimate the intervention distributions. In the absence of this domain knowledge, the causal structure must be discovered from the available observational data. However, observational data are often compatible with multiple causal graphs, making methods that commit to a single structure prone to overconfidence. A principled way to manage this structural uncertainty is via Bayesian inference, which averages over a posterior distribution on possible causal structures and functional mechanisms. Unfortunately, the number of causal structures grows super-exponentially with the number of nodes in the graph, making computations intractable. We propose to circumvent these challenges by using meta-learning to create an end-to-end model: the Model-Averaged Causal Estimation Transformer Neural Process (MACE-TNP). The model is trained to predict the Bayesian model-averaged interventional posterior distribution, and its end-to-end nature bypasses the need for expensive calculations. Empirically, we demonstrate that MACE-TNP outperforms strong Bayesian baselines. Our work establishes meta-learning as a flexible and scalable paradigm for approximating complex Bayesian causal inference, that can be scaled to increasingly challenging settings in the future. △ Less

Submitted 10 February, 2026; v1 submitted 7 July, 2025; originally announced July 2025.

Distributional Training Data Attribution: What do Influence Functions Sample?

Authors: Bruno Mlodozeniec, Isaac Reid, Sam Power, David Krueger, Murat Erdogdu, Richard E. Turner, Roger Grosse

Abstract: Randomness is an unavoidable part of training deep learning models, yet something that traditional training data attribution algorithms fail to rigorously account for. They ignore the fact that, due to stochasticity in the initialisation and batching, training on the same dataset can yield different models. In this paper, we address this shortcoming through introducing distributional training data… ▽ More Randomness is an unavoidable part of training deep learning models, yet something that traditional training data attribution algorithms fail to rigorously account for. They ignore the fact that, due to stochasticity in the initialisation and batching, training on the same dataset can yield different models. In this paper, we address this shortcoming through introducing distributional training data attribution (d-TDA), the goal of which is to predict how the distribution of model outputs (over training runs) depends upon the dataset. Intriguingly, we find that influence functions (IFs), a popular data attribution tool, are 'secretly distributional': they emerge from our framework as the limit to unrolled differentiation, without requiring restrictive convexity assumptions. This provides a new perspective on the effectiveness of IFs in deep learning. We demonstrate the practical utility of d-TDA in experiments, including improving data pruning for vision transformers and identifying influential examples with diffusion models. △ Less

Submitted 25 October, 2025; v1 submitted 15 June, 2025; originally announced June 2025.

Purifying Shampoo: Investigating Shampoo's Heuristics by Decomposing its Preconditioner

Authors: Runa Eschenhagen, Aaron Defazio, Tsung-Hsien Lee, Richard E. Turner, Hao-Jun Michael Shi

Abstract: The recent success of Shampoo in the AlgoPerf contest has sparked renewed interest in Kronecker-factorization-based optimization algorithms for training neural networks. Despite its success, Shampoo relies heavily on several heuristics such as learning rate grafting and stale preconditioning to achieve performance at-scale. These heuristics increase algorithmic complexity, necessitate further hype… ▽ More The recent success of Shampoo in the AlgoPerf contest has sparked renewed interest in Kronecker-factorization-based optimization algorithms for training neural networks. Despite its success, Shampoo relies heavily on several heuristics such as learning rate grafting and stale preconditioning to achieve performance at-scale. These heuristics increase algorithmic complexity, necessitate further hyperparameter tuning, and lack theoretical justification. This paper investigates these heuristics from the angle of Frobenius norm approximation to full-matrix Adam and decouples the preconditioner's eigenvalues and eigenbasis updates. We show that grafting from Adam mitigates the staleness and mis-scaling of the preconditioner's eigenvalues and how correcting the eigenvalues directly eliminates the need for learning rate grafting. To manage the error induced by infrequent eigenbasis computations, we propose an adaptive criterion for determining the eigenbasis computation frequency motivated by terminating a warm-started QR algorithm. This criterion decouples the update frequency of different preconditioner matrices and enables us to investigate the impact of approximation error on convergence. These practical techniques offer a principled angle towards removing Shampoo's heuristics and developing improved Kronecker-factorization-based training algorithms. △ Less

Submitted 29 October, 2025; v1 submitted 4 June, 2025; originally announced June 2025.

Comments: NeurIPS 2025

JoLT: Joint Probabilistic Predictions on Tabular Data Using LLMs

Authors: Aliaksandra Shysheya, John Bronskill, James Requeima, Shoaib Ahmed Siddiqui, Javier Gonzalez, David Duvenaud, Richard E. Turner

Abstract: We introduce a simple method for probabilistic predictions on tabular data based on Large Language Models (LLMs) called JoLT (Joint LLM Process for Tabular data). JoLT uses the in-context learning capabilities of LLMs to define joint distributions over tabular data conditioned on user-specified side information about the problem, exploiting the vast repository of latent problem-relevant knowledge… ▽ More We introduce a simple method for probabilistic predictions on tabular data based on Large Language Models (LLMs) called JoLT (Joint LLM Process for Tabular data). JoLT uses the in-context learning capabilities of LLMs to define joint distributions over tabular data conditioned on user-specified side information about the problem, exploiting the vast repository of latent problem-relevant knowledge encoded in LLMs. JoLT defines joint distributions for multiple target variables with potentially heterogeneous data types without any data conversion, data preprocessing, special handling of missing data, or model training, making it accessible and efficient for practitioners. Our experiments show that JoLT outperforms competitive methods on low-shot single-target and multi-target tabular classification and regression tasks. Furthermore, we show that JoLT can automatically handle missing data and perform data imputation by leveraging textual side information. We argue that due to its simplicity and generality, JoLT is an effective approach for a wide variety of real prediction problems. △ Less

Submitted 17 February, 2025; originally announced February 2025.

Spectral-factorized Positive-definite Curvature Learning for NN Training

Authors: Wu Lin, Felix Dangel, Runa Eschenhagen, Juhan Bae, Richard E. Turner, Roger B. Grosse

Abstract: Many training methods, such as Adam(W) and Shampoo, learn a positive-definite curvature matrix and apply an inverse root before preconditioning. Recently, non-diagonal training methods, such as Shampoo, have gained significant attention; however, they remain computationally inefficient and are limited to specific types of curvature information due to the costly matrix root computation via matrix d… ▽ More Many training methods, such as Adam(W) and Shampoo, learn a positive-definite curvature matrix and apply an inverse root before preconditioning. Recently, non-diagonal training methods, such as Shampoo, have gained significant attention; however, they remain computationally inefficient and are limited to specific types of curvature information due to the costly matrix root computation via matrix decomposition. To address this, we propose a Riemannian optimization approach that dynamically adapts spectral-factorized positive-definite curvature estimates, enabling the efficient application of arbitrary matrix roots and generic curvature learning. We demonstrate the efficacy and versatility of our approach in positive-definite matrix optimization and covariance adaptation for gradient-free optimization, as well as its efficiency in curvature learning for neural net training. △ Less

Submitted 28 March, 2025; v1 submitted 10 February, 2025; originally announced February 2025.

Comments: fixed some typos in the appendix

Tighter sparse variational Gaussian processes

Authors: Thang D. Bui, Matthew Ashman, Richard E. Turner

Abstract: Sparse variational Gaussian process (GP) approximations based on inducing points have become the de facto standard for scaling GPs to large datasets, owing to their theoretical elegance, computational efficiency, and ease of implementation. This paper introduces a provably tighter variational approximation by relaxing the standard assumption that the conditional approximate posterior given the ind… ▽ More Sparse variational Gaussian process (GP) approximations based on inducing points have become the de facto standard for scaling GPs to large datasets, owing to their theoretical elegance, computational efficiency, and ease of implementation. This paper introduces a provably tighter variational approximation by relaxing the standard assumption that the conditional approximate posterior given the inducing points must match that in the prior. The key innovation is to modify the conditional posterior to have smaller variances than that of the prior at the training points. We derive the collapsed bound for the regression case, describe how to use the proposed approximation in large data settings, and discuss its application to handle orthogonally structured inducing points and GP latent variable models. Extensive experiments on regression benchmarks, classification, and latent variable models demonstrate that the proposed approximation consistently matches or outperforms standard sparse variational GPs while maintaining the same computational cost. An implementation will be made available in all popular GP packages. △ Less

Submitted 13 February, 2025; v1 submitted 7 February, 2025; originally announced February 2025.

Efficient Few-Shot Continual Learning in Vision-Language Models

Authors: Aristeidis Panos, Rahaf Aljundi, Daniel Olmeda Reino, Richard E. Turner

Abstract: Vision-language models (VLMs) excel in tasks such as visual question answering and image captioning. However, VLMs are often limited by their use of pretrained image encoders, like CLIP, leading to image understanding errors that hinder overall performance. On top of that, real-world applications often require the model to be continuously adapted as new and often limited data continuously arrive.… ▽ More Vision-language models (VLMs) excel in tasks such as visual question answering and image captioning. However, VLMs are often limited by their use of pretrained image encoders, like CLIP, leading to image understanding errors that hinder overall performance. On top of that, real-world applications often require the model to be continuously adapted as new and often limited data continuously arrive. To address this, we propose LoRSU (Low-Rank Adaptation with Structured Updates), a robust and computationally efficient method for selectively updating image encoders within VLMs. LoRSU introduces structured and localized parameter updates, effectively correcting performance on previously error-prone data while preserving the model's general robustness. Our approach leverages theoretical insights to identify and update only the most critical parameters, achieving significant resource efficiency. Specifically, we demonstrate that LoRSU reduces computational overhead by over 25x compared to full VLM updates, without sacrificing performance. Experimental results on VQA tasks in the few-shot continual learning setting, validate LoRSU's scalability, efficiency, and effectiveness, making it a compelling solution for image encoder adaptation in resource-constrained environments. △ Less

Submitted 7 February, 2025; v1 submitted 6 February, 2025; originally announced February 2025.

Refined climatologies of future precipitation over High Mountain Asia using probabilistic ensemble learning

Authors: Kenza Tazi, Sun Woo P. Kim, Marc Girona-Mata, Richard E. Turner

Abstract: High Mountain Asia (HMA) holds the highest concentration of frozen water outside the polar regions, serving as a crucial water source for more than 1.9 billion people. Precipitation represents the largest source of uncertainty for future hydrological modelling in this area. In this study, we propose a probabilistic machine learning framework to combine monthly precipitation from 13 regional climat… ▽ More High Mountain Asia (HMA) holds the highest concentration of frozen water outside the polar regions, serving as a crucial water source for more than 1.9 billion people. Precipitation represents the largest source of uncertainty for future hydrological modelling in this area. In this study, we propose a probabilistic machine learning framework to combine monthly precipitation from 13 regional climate models developed under the Coordinated Regional Downscaling Experiment (CORDEX) over HMA via a mixture of experts (MoE). This approach accounts for seasonal and spatial biases within the models, enabling the prediction of more faithful precipitation distributions. The MoE is trained and validated against gridded historical precipitation data, yielding 32% improvement over an equally-weighted average and 254% improvement over choosing any single ensemble member. This approach is then used to generate precipitation projections for the near future (2036-2065) and far future (2066-2095) under RCP4.5 and RCP8.5 scenarios. Compared to previous estimates, the MoE projects wetter summers but drier winters over the western Himalayas and Karakoram and wetter winters over the Tibetan Plateau, Hengduan Shan, and South East Tibet. △ Less

Submitted 30 June, 2025; v1 submitted 26 January, 2025; originally announced January 2025.

Comments: 16 pages 8 figures (main text), 32 pages 14 figures (total)

On conditional diffusion models for PDE simulations

Authors: Aliaksandra Shysheya, Cristiana Diaconu, Federico Bergamin, Paris Perdikaris, José Miguel Hernández-Lobato, Richard E. Turner, Emile Mathieu

Abstract: Modelling partial differential equations (PDEs) is of crucial importance in science and engineering, and it includes tasks ranging from forecasting to inverse problems, such as data assimilation. However, most previous numerical and machine learning approaches that target forecasting cannot be applied out-of-the-box for data assimilation. Recently, diffusion models have emerged as a powerful tool… ▽ More Modelling partial differential equations (PDEs) is of crucial importance in science and engineering, and it includes tasks ranging from forecasting to inverse problems, such as data assimilation. However, most previous numerical and machine learning approaches that target forecasting cannot be applied out-of-the-box for data assimilation. Recently, diffusion models have emerged as a powerful tool for conditional generation, being able to flexibly incorporate observations without retraining. In this work, we perform a comparative study of score-based diffusion models for forecasting and assimilation of sparse observations. In particular, we focus on diffusion models that are either trained in a conditional manner, or conditioned after unconditional training. We address the shortcomings of existing models by proposing 1) an autoregressive sampling approach that significantly improves performance in forecasting, 2) a new training strategy for conditional score-based models that achieves stable performance over a range of history lengths, and 3) a hybrid model which employs flexible pre-training conditioning on initial conditions and flexible post-training conditioning to handle data assimilation. We empirically show that these modifications are crucial for successfully tackling the combination of forecasting and data assimilation, a task commonly encountered in real-world scenarios. △ Less

Submitted 21 October, 2024; originally announced October 2024.

Comments: Accepted at NeurIPS 2024

Gridded Transformer Neural Processes for Large Unstructured Spatio-Temporal Data

Authors: Matthew Ashman, Cristiana Diaconu, Eric Langezaal, Adrian Weller, Richard E. Turner

Abstract: Many important problems require modelling large-scale spatio-temporal datasets, with one prevalent example being weather forecasting. Recently, transformer-based approaches have shown great promise in a range of weather forecasting problems. However, these have mostly focused on gridded data sources, neglecting the wealth of unstructured, off-the-grid data from observational measurements such as t… ▽ More Many important problems require modelling large-scale spatio-temporal datasets, with one prevalent example being weather forecasting. Recently, transformer-based approaches have shown great promise in a range of weather forecasting problems. However, these have mostly focused on gridded data sources, neglecting the wealth of unstructured, off-the-grid data from observational measurements such as those at weather stations. A promising family of models suitable for such tasks are neural processes (NPs), notably the family of transformer neural processes (TNPs). Although TNPs have shown promise on small spatio-temporal datasets, they are unable to scale to the quantities of data used by state-of-the-art weather and climate models. This limitation stems from their lack of efficient attention mechanisms. We address this shortcoming through the introduction of gridded pseudo-token TNPs which employ specialised encoders and decoders to handle unstructured observations and utilise a processor containing gridded pseudo-tokens that leverage efficient attention mechanisms. Our method consistently outperforms a range of strong baselines on various synthetic and real-world regression tasks involving large-scale data, while maintaining competitive computational efficiency. The real-life experiments are performed on weather data, demonstrating the potential of our approach to bring performance and computational benefits when applied at scale in a weather modelling pipeline. △ Less

Submitted 10 October, 2024; v1 submitted 9 October, 2024; originally announced October 2024.

Linear Transformer Topological Masking with Graph Random Features

Authors: Isaac Reid, Kumar Avinava Dubey, Deepali Jain, Will Whitney, Amr Ahmed, Joshua Ainslie, Alex Bewley, Mithun Jacob, Aranyak Mehta, David Rendleman, Connor Schenck, Richard E. Turner, René Wagner, Adrian Weller, Krzysztof Choromanski

Abstract: When training transformers on graph-structured data, incorporating information about the underlying topology is crucial for good performance. Topological masking, a type of relative position encoding, achieves this by upweighting or downweighting attention depending on the relationship between the query and keys in a graph. In this paper, we propose to parameterise topological masks as a learnable… ▽ More When training transformers on graph-structured data, incorporating information about the underlying topology is crucial for good performance. Topological masking, a type of relative position encoding, achieves this by upweighting or downweighting attention depending on the relationship between the query and keys in a graph. In this paper, we propose to parameterise topological masks as a learnable function of a weighted adjacency matrix -- a novel, flexible approach which incorporates a strong structural inductive bias. By approximating this mask with graph random features (for which we prove the first known concentration bounds), we show how this can be made fully compatible with linear attention, preserving $\mathcal{O}(N)$ time and space complexity with respect to the number of input tokens. The fastest previous alternative was $\mathcal{O}(N \log N)$ and only suitable for specific graphs. Our efficient masking algorithms provide strong performance gains for tasks on image and point cloud data, including with $>30$k nodes. △ Less

Submitted 15 October, 2024; v1 submitted 4 October, 2024; originally announced October 2024.

AI for operational methane emitter monitoring from space

Authors: Anna Vaughan, Gonzalo Mateo-Garcia, Itziar Irakulis-Loitxate, Marc Watine, Pablo Fernandez-Poblaciones, Richard E. Turner, James Requeima, Javier Gorroño, Cynthia Randles, Manfredi Caltagirone, Claudio Cifarelli

Abstract: Mitigating methane emissions is the fastest way to stop global warming in the short-term and buy humanity time to decarbonise. Despite the demonstrated ability of remote sensing instruments to detect methane plumes, no system has been available to routinely monitor and act on these events. We present MARS-S2L, an automated AI-driven methane emitter monitoring system for Sentinel-2 and Landsat sate… ▽ More Mitigating methane emissions is the fastest way to stop global warming in the short-term and buy humanity time to decarbonise. Despite the demonstrated ability of remote sensing instruments to detect methane plumes, no system has been available to routinely monitor and act on these events. We present MARS-S2L, an automated AI-driven methane emitter monitoring system for Sentinel-2 and Landsat satellite imagery deployed operationally at the United Nations Environment Programme's International Methane Emissions Observatory. We compile a global dataset of thousands of super-emission events for training and evaluation, demonstrating that MARS-S2L can skillfully monitor emissions in a diverse range of regions globally, providing a 216% improvement in mean average precision over a current state-of-the-art detection method. Running this system operationally for six months has yielded 457 near-real-time detections in 22 different countries of which 62 have already been used to provide formal notifications to governments and stakeholders. △ Less

Submitted 8 August, 2024; originally announced August 2024.

Imperfect Vision Encoders: Efficient and Robust Tuning for Vision-Language Models

Authors: Aristeidis Panos, Rahaf Aljundi, Daniel Olmeda Reino, Richard E Turner

Abstract: Vision language models (VLMs) demonstrate impressive capabilities in visual question answering and image captioning, acting as a crucial link between visual and language models. However, existing open-source VLMs heavily rely on pretrained and frozen vision encoders (such as CLIP). Despite CLIP's robustness across diverse domains, it still exhibits non-negligible image understanding errors. These… ▽ More Vision language models (VLMs) demonstrate impressive capabilities in visual question answering and image captioning, acting as a crucial link between visual and language models. However, existing open-source VLMs heavily rely on pretrained and frozen vision encoders (such as CLIP). Despite CLIP's robustness across diverse domains, it still exhibits non-negligible image understanding errors. These errors propagate to the VLM responses, resulting in sub-optimal performance. In our work, we propose an efficient and robust method for updating vision encoders within VLMs. Our approach selectively and locally updates encoders, leading to substantial performance improvements on data where previous mistakes occurred, while maintaining overall robustness. Furthermore, we demonstrate the effectiveness of our method during continual few-shot updates. Theoretical grounding, generality, and computational efficiency characterize our approach. △ Less

Submitted 23 July, 2024; originally announced July 2024.

In-Context In-Context Learning with Transformer Neural Processes

Authors: Matthew Ashman, Cristiana Diaconu, Adrian Weller, Richard E. Turner

Abstract: Neural processes (NPs) are a powerful family of meta-learning models that seek to approximate the posterior predictive map of the ground-truth stochastic process from which each dataset in a meta-dataset is sampled. There are many cases in which practitioners, besides having access to the dataset of interest, may also have access to other datasets that share similarities with it. In this case, int… ▽ More Neural processes (NPs) are a powerful family of meta-learning models that seek to approximate the posterior predictive map of the ground-truth stochastic process from which each dataset in a meta-dataset is sampled. There are many cases in which practitioners, besides having access to the dataset of interest, may also have access to other datasets that share similarities with it. In this case, integrating these datasets into the NP can improve predictions. We equip NPs with this functionality and describe this paradigm as in-context in-context learning. Standard NP architectures, such as the convolutional conditional NP (ConvCNP) or the family of transformer neural processes (TNPs), are not capable of in-context in-context learning, as they are only able to condition on a single dataset. We address this shortcoming by developing the in-context in-context learning pseudo-token TNP (ICICL-TNP). The ICICL-TNP builds on the family of PT-TNPs, which utilise pseudo-token-based transformer architectures to sidestep the quadratic computational complexity associated with regular transformer architectures. Importantly, the ICICL-TNP is capable of conditioning on both sets of datapoints and sets of datasets, enabling it to perform in-context in-context learning. We demonstrate the importance of in-context in-context learning and the effectiveness of the ICICL-TNP in a number of experiments. △ Less

Submitted 19 June, 2024; originally announced June 2024.

Approximately Equivariant Neural Processes

Authors: Matthew Ashman, Cristiana Diaconu, Adrian Weller, Wessel Bruinsma, Richard E. Turner

Abstract: Equivariant deep learning architectures exploit symmetries in learning problems to improve the sample efficiency of neural-network-based models and their ability to generalise. However, when modelling real-world data, learning problems are often not exactly equivariant, but only approximately. For example, when estimating the global temperature field from weather station observations, local topogr… ▽ More Equivariant deep learning architectures exploit symmetries in learning problems to improve the sample efficiency of neural-network-based models and their ability to generalise. However, when modelling real-world data, learning problems are often not exactly equivariant, but only approximately. For example, when estimating the global temperature field from weather station observations, local topographical features like mountains break translation equivariance. In these scenarios, it is desirable to construct architectures that can flexibly depart from exact equivariance in a data-driven way. Current approaches to achieving this cannot usually be applied out-of-the-box to any architecture and symmetry group. In this paper, we develop a general approach to achieving this using existing equivariant architectures. Our approach is agnostic to both the choice of symmetry group and model architecture, making it widely applicable. We consider the use of approximately equivariant architectures in neural processes (NPs), a popular family of meta-learning models. We demonstrate the effectiveness of our approach on a number of synthetic and real-world regression experiments, showing that approximately equivariant NP models can outperform both their non-equivariant and strictly equivariant counterparts. △ Less

Submitted 9 November, 2024; v1 submitted 19 June, 2024; originally announced June 2024.

Bayesian Circular Regression with von Mises Quasi-Processes

Authors: Yarden Cohen, Alexandre Khae Wu Navarro, Jes Frellsen, Richard E. Turner, Raziel Riemer, Ari Pakman

Abstract: The need for regression models to predict circular values arises in many scientific fields. In this work we explore a family of expressive and interpretable distributions over circle-valued random functions related to Gaussian processes targeting two Euclidean dimensions conditioned on the unit circle. The probability model has connections with continuous spin models in statistical physics. Moreov… ▽ More The need for regression models to predict circular values arises in many scientific fields. In this work we explore a family of expressive and interpretable distributions over circle-valued random functions related to Gaussian processes targeting two Euclidean dimensions conditioned on the unit circle. The probability model has connections with continuous spin models in statistical physics. Moreover, its density is very simple and has maximum-entropy, unlike previous Gaussian process-based approaches, which use wrapping or radial marginalization. For posterior inference, we introduce a new Stratonovich-like augmentation that lends itself to fast Gibbs sampling. We argue that transductive learning in these models favors a Bayesian approach to the parameters and apply our sampling scheme to the Double Metropolis-Hastings algorithm. We present experiments applying this model to the prediction of (i) wind directions and (ii) the percentage of the running gait cycle as a function of joint angles. △ Less

Submitted 18 March, 2025; v1 submitted 18 June, 2024; originally announced June 2024.

Journal ref: Proceedings of the 28th International Conference on Artificial Intelligence and Statistics (AISTATS) 2025

Translation Equivariant Transformer Neural Processes

Authors: Matthew Ashman, Cristiana Diaconu, Junhyuck Kim, Lakee Sivaraya, Stratis Markou, James Requeima, Wessel P. Bruinsma, Richard E. Turner

Abstract: The effectiveness of neural processes (NPs) in modelling posterior prediction maps -- the mapping from data to posterior predictive distributions -- has significantly improved since their inception. This improvement can be attributed to two principal factors: (1) advancements in the architecture of permutation invariant set functions, which are intrinsic to all NPs; and (2) leveraging symmetries p… ▽ More The effectiveness of neural processes (NPs) in modelling posterior prediction maps -- the mapping from data to posterior predictive distributions -- has significantly improved since their inception. This improvement can be attributed to two principal factors: (1) advancements in the architecture of permutation invariant set functions, which are intrinsic to all NPs; and (2) leveraging symmetries present in the true posterior predictive map, which are problem dependent. Transformers are a notable development in permutation invariant set functions, and their utility within NPs has been demonstrated through the family of models we refer to as TNPs. Despite significant interest in TNPs, little attention has been given to incorporating symmetries. Notably, the posterior prediction maps for data that are stationary -- a common assumption in spatio-temporal modelling -- exhibit translation equivariance. In this paper, we introduce of a new family of translation equivariant TNPs that incorporate translation equivariance. Through an extensive range of experiments on synthetic and real-world spatio-temporal data, we demonstrate the effectiveness of TE-TNPs relative to their non-translation-equivariant counterparts and other NP baselines. △ Less

Submitted 18 June, 2024; originally announced June 2024.

Noise-Aware Differentially Private Regression via Meta-Learning

Authors: Ossi Räisä, Stratis Markou, Matthew Ashman, Wessel P. Bruinsma, Marlon Tobaben, Antti Honkela, Richard E. Turner

Abstract: Many high-stakes applications require machine learning models that protect user privacy and provide well-calibrated, accurate predictions. While Differential Privacy (DP) is the gold standard for protecting user privacy, standard DP mechanisms typically significantly impair performance. One approach to mitigating this issue is pre-training models on simulated data before DP learning on the private… ▽ More Many high-stakes applications require machine learning models that protect user privacy and provide well-calibrated, accurate predictions. While Differential Privacy (DP) is the gold standard for protecting user privacy, standard DP mechanisms typically significantly impair performance. One approach to mitigating this issue is pre-training models on simulated data before DP learning on the private data. In this work we go a step further, using simulated data to train a meta-learning model that combines the Convolutional Conditional Neural Process (ConvCNP) with an improved functional DP mechanism of Hall et al. [2013] yielding the DPConvCNP. DPConvCNP learns from simulated data how to map private data to a DP predictive model in one forward pass, and then provides accurate, well-calibrated predictions. We compare DPConvCNP with a DP Gaussian Process (GP) baseline with carefully tuned hyperparameters. The DPConvCNP outperforms the GP baseline, especially on non-Gaussian data, yet is much faster at test time and requires less tuning. △ Less

Submitted 8 May, 2025; v1 submitted 12 June, 2024; originally announced June 2024.

Comments: NeurIPS 2024

Fearless Stochasticity in Expectation Propagation

Authors: Jonathan So, Richard E. Turner

Abstract: Expectation propagation (EP) is a family of algorithms for performing approximate inference in probabilistic models. The updates of EP involve the evaluation of moments -- expectations of certain functions -- which can be estimated from Monte Carlo (MC) samples. However, the updates are not robust to MC noise when performed naively, and various prior works have attempted to address this issue in d… ▽ More Expectation propagation (EP) is a family of algorithms for performing approximate inference in probabilistic models. The updates of EP involve the evaluation of moments -- expectations of certain functions -- which can be estimated from Monte Carlo (MC) samples. However, the updates are not robust to MC noise when performed naively, and various prior works have attempted to address this issue in different ways. In this work, we provide a novel perspective on the moment-matching updates of EP; namely, that they perform natural-gradient-based optimisation of a variational objective. We use this insight to motivate two new EP variants, with updates that are particularly well-suited to MC estimation. They remain stable and are most sample-efficient when estimated with just a single sample. These new variants combine the benefits of their predecessors and address key weaknesses. In particular, they are easier to tune, offer an improved speed-accuracy trade-off, and do not rely on the use of debiasing estimators. We demonstrate their efficacy on a variety of probabilistic inference tasks. △ Less

Submitted 29 October, 2024; v1 submitted 3 June, 2024; originally announced June 2024.

Variance-Reducing Couplings for Random Features

Authors: Isaac Reid, Stratis Markou, Krzysztof Choromanski, Richard E. Turner, Adrian Weller

Abstract: Random features (RFs) are a popular technique to scale up kernel methods in machine learning, replacing exact kernel evaluations with stochastic Monte Carlo estimates. They underpin models as diverse as efficient transformers (by approximating attention) to sparse spectrum Gaussian processes (by approximating the covariance function). Efficiency can be further improved by speeding up the convergen… ▽ More Random features (RFs) are a popular technique to scale up kernel methods in machine learning, replacing exact kernel evaluations with stochastic Monte Carlo estimates. They underpin models as diverse as efficient transformers (by approximating attention) to sparse spectrum Gaussian processes (by approximating the covariance function). Efficiency can be further improved by speeding up the convergence of these estimates: a variance reduction problem. We tackle this through the unifying lens of optimal transport, finding couplings to improve RFs defined on both Euclidean and discrete input spaces. They enjoy theoretical guarantees and sometimes provide strong downstream gains, including for scalable approximate inference on graphs. We reach surprising conclusions about the benefits and limitations of variance reduction as a paradigm, showing that other properties of the coupling should be optimised for attention estimation in efficient transformers. △ Less

Submitted 2 October, 2024; v1 submitted 26 May, 2024; originally announced May 2024.

A Foundation Model for the Earth System

Authors: Cristian Bodnar, Wessel P. Bruinsma, Ana Lucic, Megan Stanley, Anna Vaughan, Johannes Brandstetter, Patrick Garvan, Maik Riechert, Jonathan A. Weyn, Haiyu Dong, Jayesh K. Gupta, Kit Thambiratnam, Alexander T. Archibald, Chun-Chieh Wu, Elizabeth Heider, Max Welling, Richard E. Turner, Paris Perdikaris

Abstract: Reliable forecasts of the Earth system are crucial for human progress and safety from natural disasters. Artificial intelligence offers substantial potential to improve prediction accuracy and computational efficiency in this field, however this remains underexplored in many domains. Here we introduce Aurora, a large-scale foundation model for the Earth system trained on over a million hours of di… ▽ More Reliable forecasts of the Earth system are crucial for human progress and safety from natural disasters. Artificial intelligence offers substantial potential to improve prediction accuracy and computational efficiency in this field, however this remains underexplored in many domains. Here we introduce Aurora, a large-scale foundation model for the Earth system trained on over a million hours of diverse data. Aurora outperforms operational forecasts for air quality, ocean waves, tropical cyclone tracks, and high-resolution weather forecasting at orders of magnitude smaller computational expense than dedicated existing systems. With the ability to fine-tune Aurora to diverse application domains at only modest computational cost, Aurora represents significant progress in making actionable Earth system predictions accessible to anyone. △ Less

Submitted 21 November, 2024; v1 submitted 20 May, 2024; originally announced May 2024.

LLM Processes: Numerical Predictive Distributions Conditioned on Natural Language

Authors: James Requeima, John Bronskill, Dami Choi, Richard E. Turner, David Duvenaud

Abstract: Machine learning practitioners often face significant challenges in formally integrating their prior knowledge and beliefs into predictive models, limiting the potential for nuanced and context-aware analyses. Moreover, the expertise needed to integrate this prior knowledge into probabilistic modeling typically limits the application of these models to specialists. Our goal is to build a regressio… ▽ More Machine learning practitioners often face significant challenges in formally integrating their prior knowledge and beliefs into predictive models, limiting the potential for nuanced and context-aware analyses. Moreover, the expertise needed to integrate this prior knowledge into probabilistic modeling typically limits the application of these models to specialists. Our goal is to build a regression model that can process numerical data and make probabilistic predictions at arbitrary locations, guided by natural language text which describes a user's prior knowledge. Large Language Models (LLMs) provide a useful starting point for designing such a tool since they 1) provide an interface where users can incorporate expert insights in natural language and 2) provide an opportunity for leveraging latent problem-relevant knowledge encoded in LLMs that users may not have themselves. We start by exploring strategies for eliciting explicit, coherent numerical predictive distributions from LLMs. We examine these joint predictive distributions, which we call LLM Processes, over arbitrarily-many quantities in settings such as forecasting, multi-dimensional regression, black-box optimization, and image modeling. We investigate the practical details of prompting to elicit coherent predictive distributions, and demonstrate their effectiveness at regression. Finally, we demonstrate the ability to usefully incorporate text into numerical predictions, improving predictive performance and giving quantitative structure that reflects qualitative descriptions. This lets us begin to explore the rich, grounded hypothesis space that LLMs implicitly encode. △ Less

Submitted 19 December, 2024; v1 submitted 21 May, 2024; originally announced May 2024.

Journal ref: 38th Conference on Neural Information Processing Systems (NeurIPS 2024)

Aardvark weather: end-to-end data-driven weather forecasting

Authors: Anna Vaughan, Stratis Markou, Will Tebbutt, James Requeima, Wessel P. Bruinsma, Tom R. Andersson, Michael Herzog, Nicholas D. Lane, Matthew Chantry, J. Scott Hosking, Richard E. Turner

Abstract: Weather forecasting is critical for a range of human activities including transportation, agriculture, industry, as well as the safety of the general public. Machine learning models have the potential to transform the complex weather prediction pipeline, but current approaches still rely on numerical weather prediction (NWP) systems, limiting forecast speed and accuracy. Here we demonstrate that a… ▽ More Weather forecasting is critical for a range of human activities including transportation, agriculture, industry, as well as the safety of the general public. Machine learning models have the potential to transform the complex weather prediction pipeline, but current approaches still rely on numerical weather prediction (NWP) systems, limiting forecast speed and accuracy. Here we demonstrate that a machine learning model can replace the entire operational NWP pipeline. Aardvark Weather, an end-to-end data-driven weather prediction system, ingests raw observations and outputs global gridded forecasts and local station forecasts. Further, it can be optimised end-to-end to maximise performance over quantities of interest. Global forecasts outperform an operational NWP baseline for multiple variables and lead times. Local station forecasts are skillful up to ten days lead time and achieve comparable and often lower errors than a post-processed global NWP baseline and a state-of-the-art end-to-end forecasting system with input from human forecasters. These forecasts are produced with a remarkably simple neural process model using just 8% of the input data and three orders of magnitude less compute than existing NWP and hybrid AI-NWP methods. We anticipate that Aardvark Weather will be the starting point for a new generation of end-to-end machine learning models for medium-range forecasting that will reduce computational costs by orders of magnitude and enable the rapid and cheap creation of bespoke models for users in a variety of fields, including for the developing world where state-of-the-art local models are not currently available. △ Less

Submitted 13 July, 2024; v1 submitted 30 March, 2024; originally announced April 2024.

SportsNGEN: Sustained Generation of Realistic Multi-player Sports Gameplay

Authors: Lachlan Thorpe, Lewis Bawden, Karanjot Vendal, John Bronskill, Richard E. Turner

Abstract: We present a transformer decoder based sports simulation engine, SportsNGEN, trained on sports player and ball tracking sequences, that is capable of generating sustained gameplay and accurately mimicking the decision making of real players. By training on a large database of professional tennis tracking data, we demonstrate that simulations produced by SportsNGEN can be used to predict the outcom… ▽ More We present a transformer decoder based sports simulation engine, SportsNGEN, trained on sports player and ball tracking sequences, that is capable of generating sustained gameplay and accurately mimicking the decision making of real players. By training on a large database of professional tennis tracking data, we demonstrate that simulations produced by SportsNGEN can be used to predict the outcomes of rallies, determine the best shot choices at any point, and evaluate counterfactual or what if scenarios to inform coaching decisions and elevate broadcast coverage. By combining the generated simulations with a shot classifier and logic to start and end rallies, the system is capable of simulating an entire tennis match. We evaluate SportsNGEN by comparing statistics of the simulations with those of real matches between the same players. We show that the model output sampling parameters are crucial to simulation realism and that SportsNGEN is probabilistically well-calibrated to real data. In addition, a generic version of SportsNGEN can be customized to a specific player by fine-tuning on the subset of match data that includes that player. Finally, we show qualitative results indicating the same approach works for football. △ Less

Submitted 18 November, 2024; v1 submitted 9 February, 2024; originally announced March 2024.

Journal ref: Proceedings of the 12th International Conference on Sport Sciences Research and Technology Support (icSPORTS 2024)

A Generative Model of Symmetry Transformations

Authors: James Urquhart Allingham, Bruno Kacper Mlodozeniec, Shreyas Padhy, Javier Antorán, David Krueger, Richard E. Turner, Eric Nalisnick, José Miguel Hernández-Lobato

Abstract: Correctly capturing the symmetry transformations of data can lead to efficient models with strong generalization capabilities, though methods incorporating symmetries often require prior knowledge. While recent advancements have been made in learning those symmetries directly from the dataset, most of this work has focused on the discriminative setting. In this paper, we take inspiration from grou… ▽ More Correctly capturing the symmetry transformations of data can lead to efficient models with strong generalization capabilities, though methods incorporating symmetries often require prior knowledge. While recent advancements have been made in learning those symmetries directly from the dataset, most of this work has focused on the discriminative setting. In this paper, we take inspiration from group theoretic ideas to construct a generative model that explicitly aims to capture the data's approximate symmetries. This results in a model that, given a prespecified but broad set of possible symmetries, learns to what extent, if at all, those symmetries are actually present. Our model can be seen as a generative process for data augmentation. We provide a simple algorithm for learning our generative model and empirically demonstrate its ability to capture symmetries under affine and color transformations, in an interpretable way. Combining our symmetry model with standard generative models results in higher marginal test-log-likelihoods and improved data efficiency. △ Less

Submitted 2 December, 2024; v1 submitted 4 March, 2024; originally announced March 2024.

Comments: Accepted at NeurIPS 2024

Denoising Diffusion Probabilistic Models in Six Simple Steps

Authors: Richard E. Turner, Cristiana-Diana Diaconu, Stratis Markou, Aliaksandra Shysheya, Andrew Y. K. Foong, Bruno Mlodozeniec

Abstract: Denoising Diffusion Probabilistic Models (DDPMs) are a very popular class of deep generative model that have been successfully applied to a diverse range of problems including image and video generation, protein and material synthesis, weather forecasting, and neural surrogates of partial differential equations. Despite their ubiquity it is hard to find an introduction to DDPMs which is simple, co… ▽ More Denoising Diffusion Probabilistic Models (DDPMs) are a very popular class of deep generative model that have been successfully applied to a diverse range of problems including image and video generation, protein and material synthesis, weather forecasting, and neural surrogates of partial differential equations. Despite their ubiquity it is hard to find an introduction to DDPMs which is simple, comprehensive, clean and clear. The compact explanations necessary in research papers are not able to elucidate all of the different design steps taken to formulate the DDPM and the rationale of the steps that are presented is often omitted to save space. Moreover, the expositions are typically presented from the variational lower bound perspective which is unnecessary and arguably harmful as it obfuscates why the method is working and suggests generalisations that do not perform well in practice. On the other hand, perspectives that take the continuous time-limit are beautiful and general, but they have a high barrier-to-entry as they require background knowledge of stochastic differential equations and probability flow. In this note, we distill down the formulation of the DDPM into six simple steps each of which comes with a clear rationale. We assume that the reader is familiar with fundamental topics in machine learning including basic probabilistic modelling, Gaussian distributions, maximum likelihood estimation, and deep learning. △ Less

Submitted 10 February, 2024; v1 submitted 6 February, 2024; originally announced February 2024.

Can We Remove the Square-Root in Adaptive Gradient Methods? A Second-Order Perspective

Authors: Wu Lin, Felix Dangel, Runa Eschenhagen, Juhan Bae, Richard E. Turner, Alireza Makhzani

Abstract: Adaptive gradient optimizers like Adam(W) are the default training algorithms for many deep learning architectures, such as transformers. Their diagonal preconditioner is based on the gradient outer product which is incorporated into the parameter update via a square root. While these methods are often motivated as approximate second-order methods, the square root represents a fundamental differen… ▽ More Adaptive gradient optimizers like Adam(W) are the default training algorithms for many deep learning architectures, such as transformers. Their diagonal preconditioner is based on the gradient outer product which is incorporated into the parameter update via a square root. While these methods are often motivated as approximate second-order methods, the square root represents a fundamental difference. In this work, we investigate how the behavior of adaptive methods changes when we remove the root, i.e., strengthen their second-order motivation. Surprisingly, we find that such square-root-free adaptive methods close the generalization gap to SGD on convolutional architectures, while maintaining their root-based counterpart's performance on transformers. The second-order perspective also has practical benefits for developing non-diagonal methods that can incorporate arbitrary curvature approximations through the concept of preconditioner invariance. In contrast to root-based methods like Shampoo, root-free counterparts work well and fast with half-precision since they do not require numerically unstable matrix root decompositions and inversions. Overall, our findings provide new insights into the development of adaptive methods and raise important questions regarding the overlooked role of adaptivity in their success. (experiment code: https://github.com/yorkerlin/remove-the-square-root optimizer code: https://github.com/f-dangel/sirfshampoo) △ Less

Submitted 4 October, 2024; v1 submitted 5 February, 2024; originally announced February 2024.

Comments: A long version of the ICML 2024 paper. Updated the caption of Fig 4 to emphasize the importance of the scale invariance of root-free methods

Transformer Neural Autoregressive Flows

Authors: Massimiliano Patacchiola, Aliaksandra Shysheya, Katja Hofmann, Richard E. Turner

Abstract: Density estimation, a central problem in machine learning, can be performed using Normalizing Flows (NFs). NFs comprise a sequence of invertible transformations, that turn a complex target distribution into a simple one, by exploiting the change of variables theorem. Neural Autoregressive Flows (NAFs) and Block Neural Autoregressive Flows (B-NAFs) are arguably the most perfomant members of the NF… ▽ More Density estimation, a central problem in machine learning, can be performed using Normalizing Flows (NFs). NFs comprise a sequence of invertible transformations, that turn a complex target distribution into a simple one, by exploiting the change of variables theorem. Neural Autoregressive Flows (NAFs) and Block Neural Autoregressive Flows (B-NAFs) are arguably the most perfomant members of the NF family. However, they suffer scalability issues and training instability due to the constraints imposed on the network structure. In this paper, we propose a novel solution to these challenges by exploiting transformers to define a new class of neural flows called Transformer Neural Autoregressive Flows (T-NAFs). T-NAFs treat each dimension of a random variable as a separate input token, using attention masking to enforce an autoregressive constraint. We take an amortization-inspired approach where the transformer outputs the parameters of an invertible transformation. The experimental results demonstrate that T-NAFs consistently match or outperform NAFs and B-NAFs across multiple datasets from the UCI benchmark. Remarkably, T-NAFs achieve these results using an order of magnitude fewer parameters than previous approaches, without composing multiple flows. △ Less

Submitted 3 January, 2024; originally announced January 2024.

Structured Inverse-Free Natural Gradient: Memory-Efficient & Numerically-Stable KFAC

Authors: Wu Lin, Felix Dangel, Runa Eschenhagen, Kirill Neklyudov, Agustinus Kristiadi, Richard E. Turner, Alireza Makhzani

Abstract: Second-order methods such as KFAC can be useful for neural net training. However, they are often memory-inefficient since their preconditioning Kronecker factors are dense, and numerically unstable in low precision as they require matrix inversion or decomposition. These limitations render such methods unpopular for modern mixed-precision training. We address them by (i) formulating an inverse-fre… ▽ More Second-order methods such as KFAC can be useful for neural net training. However, they are often memory-inefficient since their preconditioning Kronecker factors are dense, and numerically unstable in low precision as they require matrix inversion or decomposition. These limitations render such methods unpopular for modern mixed-precision training. We address them by (i) formulating an inverse-free KFAC update and (ii) imposing structures in the Kronecker factors, resulting in structured inverse-free natural gradient descent (SINGD). On modern neural networks, we show that SINGD is memory-efficient and numerically robust, in contrast to KFAC, and often outperforms AdamW even in half precision. Our work closes a gap between first- and second-order methods in modern low-precision training. △ Less

Submitted 23 July, 2024; v1 submitted 9 December, 2023; originally announced December 2023.

Comments: A long version of the ICML 2024 paper, updated the text about a related work

Identifiable Feature Learning for Spatial Data with Nonlinear ICA

Authors: Hermanni Hälvä, Jonathan So, Richard E. Turner, Aapo Hyvärinen

Abstract: Recently, nonlinear ICA has surfaced as a popular alternative to the many heuristic models used in deep representation learning and disentanglement. An advantage of nonlinear ICA is that a sophisticated identifiability theory has been developed; in particular, it has been proven that the original components can be recovered under sufficiently strong latent dependencies. Despite this general theory… ▽ More Recently, nonlinear ICA has surfaced as a popular alternative to the many heuristic models used in deep representation learning and disentanglement. An advantage of nonlinear ICA is that a sophisticated identifiability theory has been developed; in particular, it has been proven that the original components can be recovered under sufficiently strong latent dependencies. Despite this general theory, practical nonlinear ICA algorithms have so far been mainly limited to data with one-dimensional latent dependencies, especially time-series data. In this paper, we introduce a new nonlinear ICA framework that employs $t$-process (TP) latent components which apply naturally to data with higher-dimensional dependency structures, such as spatial and spatio-temporal data. In particular, we develop a new learning and inference algorithm that extends variational inference methods to handle the combination of a deep neural network mixing function with the TP prior, and employs the method of inducing points for computational efficacy. On the theoretical side, we show that such TP independent components are identifiable under very general conditions. Further, Gaussian Process (GP) nonlinear ICA is established as a limit of the TP Nonlinear ICA model, and we prove that the identifiability of the latent components at this GP limit is more restricted. Namely, those components are identifiable if and only if they have distinctly different covariance kernels. Our algorithm and identifiability theorems are explored on simulated spatial data and real world spatio-temporal data. △ Less

Submitted 28 November, 2023; originally announced November 2023.

Comments: Work under review

Diffusion-Augmented Neural Processes

Authors: Lorenzo Bonito, James Requeima, Aliaksandra Shysheya, Richard E. Turner

Abstract: Over the last few years, Neural Processes have become a useful modelling tool in many application areas, such as healthcare and climate sciences, in which data are scarce and prediction uncertainty estimates are indispensable. However, the current state of the art in the field (AR CNPs; Bruinsma et al., 2023) presents a few issues that prevent its widespread deployment. This work proposes an alter… ▽ More Over the last few years, Neural Processes have become a useful modelling tool in many application areas, such as healthcare and climate sciences, in which data are scarce and prediction uncertainty estimates are indispensable. However, the current state of the art in the field (AR CNPs; Bruinsma et al., 2023) presents a few issues that prevent its widespread deployment. This work proposes an alternative, diffusion-based approach to NPs which, through conditioning on noised datasets, addresses many of these limitations, whilst also exceeding SOTA performance. △ Less

Submitted 16 November, 2023; originally announced November 2023.

Comments: Accepted to the NeurIPS 2023 Workshop on Diffusion Models

ACM Class: I.2.6

Kronecker-Factored Approximate Curvature for Modern Neural Network Architectures

Authors: Runa Eschenhagen, Alexander Immer, Richard E. Turner, Frank Schneider, Philipp Hennig

Abstract: The core components of many modern neural network architectures, such as transformers, convolutional, or graph neural networks, can be expressed as linear layers with $\textit{weight-sharing}$. Kronecker-Factored Approximate Curvature (K-FAC), a second-order optimisation method, has shown promise to speed up neural network training and thereby reduce computational costs. However, there is currentl… ▽ More The core components of many modern neural network architectures, such as transformers, convolutional, or graph neural networks, can be expressed as linear layers with $\textit{weight-sharing}$. Kronecker-Factored Approximate Curvature (K-FAC), a second-order optimisation method, has shown promise to speed up neural network training and thereby reduce computational costs. However, there is currently no framework to apply it to generic architectures, specifically ones with linear weight-sharing layers. In this work, we identify two different settings of linear weight-sharing layers which motivate two flavours of K-FAC -- $\textit{expand}$ and $\textit{reduce}$. We show that they are exact for deep linear networks with weight-sharing in their respective setting. Notably, K-FAC-reduce is generally faster than K-FAC-expand, which we leverage to speed up automatic hyperparameter selection via optimising the marginal likelihood for a Wide ResNet. Finally, we observe little difference between these two K-FAC variations when using them to train both a graph neural network and a vision transformer. However, both variations are able to reach a fixed validation metric target in $50$-$75\%$ of the number of steps of a first-order reference run, which translates into a comparable improvement in wall-clock time. This highlights the potential of applying K-FAC to modern neural network architectures. △ Less

Submitted 11 January, 2024; v1 submitted 1 November, 2023; originally announced November 2023.

Comments: NeurIPS 2023

Sim2Real for Environmental Neural Processes

Authors: Jonas Scholz, Tom R. Andersson, Anna Vaughan, James Requeima, Richard E. Turner

Abstract: Machine learning (ML)-based weather models have recently undergone rapid improvements. These models are typically trained on gridded reanalysis data from numerical data assimilation systems. However, reanalysis data comes with limitations, such as assumptions about physical laws and low spatiotemporal resolution. The gap between reanalysis and reality has sparked growing interest in training ML mo… ▽ More Machine learning (ML)-based weather models have recently undergone rapid improvements. These models are typically trained on gridded reanalysis data from numerical data assimilation systems. However, reanalysis data comes with limitations, such as assumptions about physical laws and low spatiotemporal resolution. The gap between reanalysis and reality has sparked growing interest in training ML models directly on observations such as weather stations. Modelling scattered and sparse environmental observations requires scalable and flexible ML architectures, one of which is the convolutional conditional neural process (ConvCNP). ConvCNPs can learn to condition on both gridded and off-the-grid context data to make uncertainty-aware predictions at target locations. However, the sparsity of real observations presents a challenge for data-hungry deep learning models like the ConvCNP. One potential solution is 'Sim2Real': pre-training on reanalysis and fine-tuning on observational data. We analyse Sim2Real with a ConvCNP trained to interpolate surface air temperature over Germany, using varying numbers of weather stations for fine-tuning. On held-out weather stations, Sim2Real training substantially outperforms the same model architecture trained only with reanalysis data or only with station data, showing that reanalysis data can serve as a stepping stone for learning from real observations. Sim2Real could thus enable more accurate models for weather prediction and climate monitoring. △ Less

Submitted 30 October, 2023; originally announced October 2023.

Comments: 4 pages, 3 figures, To be published in Tackling Climate Change with Machine Learning workshop at NeurIPS

Optimising Distributions with Natural Gradient Surrogates

Authors: Jonathan So, Richard E. Turner

Abstract: Natural gradient methods have been used to optimise the parameters of probability distributions in a variety of settings, often resulting in fast-converging procedures. Unfortunately, for many distributions of interest, computing the natural gradient has a number of challenges. In this work we propose a novel technique for tackling such issues, which involves reframing the optimisation as one with… ▽ More Natural gradient methods have been used to optimise the parameters of probability distributions in a variety of settings, often resulting in fast-converging procedures. Unfortunately, for many distributions of interest, computing the natural gradient has a number of challenges. In this work we propose a novel technique for tackling such issues, which involves reframing the optimisation as one with respect to the parameters of a surrogate distribution, for which computing the natural gradient is easy. We give several examples of existing methods that can be interpreted as applying this technique, and propose a new method for applying it to a wide variety of problems. Our method expands the set of distributions that can be efficiently targeted with natural gradients. Furthermore, it is fast, easy to understand, simple to implement using standard autodiff software, and does not require lengthy model-specific derivations. We demonstrate our method on maximum likelihood estimation and variational inference tasks. △ Less

Submitted 4 March, 2024; v1 submitted 18 October, 2023; originally announced October 2023.

Journal ref: PMLR 238 (2024):2224-2232

PDE-Refiner: Achieving Accurate Long Rollouts with Neural PDE Solvers

Authors: Phillip Lippe, Bastiaan S. Veeling, Paris Perdikaris, Richard E. Turner, Johannes Brandstetter

Abstract: Time-dependent partial differential equations (PDEs) are ubiquitous in science and engineering. Recently, mostly due to the high computational cost of traditional solution techniques, deep neural network based surrogates have gained increased interest. The practical utility of such neural PDE solvers relies on their ability to provide accurate, stable predictions over long time horizons, which is… ▽ More Time-dependent partial differential equations (PDEs) are ubiquitous in science and engineering. Recently, mostly due to the high computational cost of traditional solution techniques, deep neural network based surrogates have gained increased interest. The practical utility of such neural PDE solvers relies on their ability to provide accurate, stable predictions over long time horizons, which is a notoriously hard problem. In this work, we present a large-scale analysis of common temporal rollout strategies, identifying the neglect of non-dominant spatial frequency information, often associated with high frequencies in PDE solutions, as the primary pitfall limiting stable, accurate rollout performance. Based on these insights, we draw inspiration from recent advances in diffusion models to introduce PDE-Refiner; a novel model class that enables more accurate modeling of all frequency components via a multistep refinement process. We validate PDE-Refiner on challenging benchmarks of complex fluid dynamics, demonstrating stable and accurate rollouts that consistently outperform state-of-the-art models, including neural, numerical, and hybrid neural-numerical architectures. We further demonstrate that PDE-Refiner greatly enhances data efficiency, since the denoising objective implicitly induces a novel form of spectral data augmentation. Finally, PDE-Refiner's connection to diffusion models enables an accurate and efficient assessment of the model's predictive uncertainty, allowing us to estimate when the surrogate becomes inaccurate. △ Less

Submitted 21 October, 2023; v1 submitted 10 August, 2023; originally announced August 2023.

Comments: Project website: https://phlippe.github.io/PDERefiner/